Binomial trials variance

Hi all,

I am beginning to look at some probability problems, I am completely new to college level probability, so not sure if this is in the right sub forum (maybe it should be in the basic?- guess mods will decide.)

Given a scenario where there is a true statistic - proportion voting yes in a vote denoted by , we sample people from the large population

For a binomial distribution for the sample where denotes the number of yes votes:

; since the binomial distribution is a 'sample' of the true statistic, we need to take into account the standard error:

I have multiplied by to scale the variance up from the true average.... is this correct?